1. Suppose that ak 20 for all k E N. (a) Use the arithmetic-geometric mean inequality to show that if the series a k=1 converges, then converges. k=1 k (b) If a converges, does it imply that k=1 i. 1 ak converges? k=1 ii. Ea converges?

Q: Option 2: Problem Solving You wish to invest P10,000 for a period of 5 years. Which of the following…

A: The principal amount we have is ₱10000 and the time period is 5 years.  Therefore,  P=₱10000 t=5

Q: Sara draws the 4 of hearts from a standard deck of 52 cards. Without replacing the first card, she…

A: Given, Sara draws the 4 of hearts from a standard deck of 52 cards without replacing. a) we know…

Q: 21. Show that E(-1)"+1; 2n converges n! absolutely. n=1

A:

Q: 43) Suppose that an > 0 for all n and that n=1 anbn necessarily converge? ∞ Σa an converges. Suppose…

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Q: ‘?

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Q: 2. Suppose the sequence {sn} satisfies Sn+ 1 - Sn ≤ -1/24 n² For all ne N. Prove that {sn}…

A: Given that the sequence  satisfies .The objective is to find for all ,  converges.

Q: 1. Let an = 5n 4n3 5 This sequence converges to L = 4 (a) Find the smallest N EN such that |an — L|…

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Q: 1. Prove that the sequence converges to . 2n+1

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Q: 1. If s, = v2 and sn+1 = NOTE: To show that a sequence converges we must show that is it monotone…

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